Qualitative spatial change: space-time histories and continuity

Abstract

Spatial configurations tend to change. Dealing with spatial representations often means dealing with changing representations. Change in state for qualitative spatial representation languages has been analyzed through transition graphs in which relations form conceptual neighbourhoods via potential motion. Continuity has remained an implicitly assumed notion for any such understanding of motion. The work described in this thesis is concerned with formalizing an intuitive notion of spatio-temporal continuity for a qualitative theory of spatial change. Taking over a theory for spatial regions, I extend it for space-time. A mereotopological spatio-temporal theory based on space-time histories is developed. I formalize the intuitive notion of spatio-temporal continuity and christen it strong firm continuity. Continuous transitions in mereotopology for space-time histories are investigated. For strong firm continuity, transition rules for spatio-temporal histories are formulated. The conceptual neighbourhood for the spatial representation language RCC-8 specifies which transitions are continuous, and in its original presentation was simply posited without any proof of correctness. Formal proofs for the non-existence of transitions i.e., transitions absent from the RCC-8 conceptual neighbourhood are presented here.